The most psychedelic music in The Beach Boys' discography can be found on the albums they released from 1966 through 1971.
Pet Sounds (1966): Its shimmering, speaking-to-God sound is psychedelic by default.
Friends (1968): The sound of stoner-hippie Hawaii circa 1968 -- while urban America went up in flames, by the way.
Surf's Up (1971): The birth of synthesizer-based avant-pop.
Beyond this stuff, The Beach Boys released a clutch of truly mind-bending nuggets, even if they aren't psychedelic in the strictest sense of the term. Most of them can be found on the records the band dropped from 1971 through 1980, which are quite uneven, in all honesty, but if you want to explore one in its entirety, go for 1977's Love You. It's just so strange.